Question Number 197171 by MM42 last updated on 09/Sep/23 $$\mathrm{2}^{{log}_{\mathrm{3}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)} +\mathrm{2}×\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{log}_{\mathrm{3}} \mathrm{2}} \:=\mathrm{12} \\ $$$$\Rightarrow{x}=? \\ $$$$ \\ $$ Answered by Frix…
Question Number 197157 by uchihayahia last updated on 09/Sep/23 $$ \\ $$$$\:{what}\:{is}\:{the}\:{area}\:{of}\:{triangle}\:{A}\:{and}\:{B}? \\ $$$$\:{i}\:{already}\:{found}\:{area}\:{of}\:{triangle}\:{A}\:{is}\:\mathrm{208} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$ Commented…
Question Number 197155 by otchereabdullai@gmail.com last updated on 09/Sep/23 $$\:{A}\:{bullet}\:{of}\:{mass}\:\mathrm{180}{g}\:{is}\:{fired}\: \\ $$$$\:{horizontally}\:{into}\:{a}\:{fixed}\:{wooden}\: \\ $$$$\:{block}\:{with}\:{a}\:{speed}\:{of}\:\mathrm{24}{m}/{s}.\:{if}\:{the}\: \\ $$$${bullet}\:{is}\:{brought}\:{to}\:{rest}\:{in}\:\mathrm{0}.\mathrm{4}{sec}\:{by}\:{a} \\ $$$${constant}\:{resistance},\:{calculate}\:{the} \\ $$$${distance}\:{moved}\:{by}\:{the}\:{bullet}\:{in}\:{the} \\ $$$${wood} \\ $$ Answered…
Question Number 197112 by sonukgindia last updated on 08/Sep/23 Answered by AST last updated on 08/Sep/23 $$\mathrm{2}{x}=\mathrm{1135}−{y}\Rightarrow\mathrm{2}{y}+\mathrm{4}{z}=\mathrm{890}\Rightarrow{y}+\mathrm{2}{z}=\mathrm{445} \\ $$$${x}=\mathrm{345}+{z},{y}=\mathrm{445}−\mathrm{2}{z},{z}={z} \\ $$$$\Rightarrow{No}\:{unique}\:{solutions} \\ $$ Commented by…
Question Number 197113 by Erico last updated on 08/Sep/23 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:+\infty} \left(\frac{{ln}\left({t}+\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\right)}{{t}}\right){dt}=\frac{\pi^{\mathrm{2}} }{\mathrm{2}} \\ $$ Answered by witcher3 last updated on 08/Sep/23…
Question Number 197146 by hardmath last updated on 08/Sep/23 $$\mathrm{Find}:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{Li}\left(\mathrm{x}\right)}{\Psi\left(\mathrm{x}\right)}\:\mathrm{dx}\:=\:? \\ $$ Answered by Blackpanther last updated on 09/Sep/23 $$\mathrm{0}.\mathrm{7823} \\ $$ Terms…
Question Number 197147 by sonukgindia last updated on 08/Sep/23 Answered by Frix last updated on 10/Sep/23 $$\mathrm{Obviously}\:{x}=\mathrm{1}\vee{x}=\frac{\pi}{\mathrm{2}}\vee{x}=\frac{\mathrm{5}\pi}{\mathrm{2}}\:\mathrm{because} \\ $$$$\mathrm{ln}\:\mathrm{1}\:=\mathrm{0}\:\mathrm{and}\:\mathrm{sin}\:\frac{\pi}{\mathrm{2}}\:=\mathrm{1} \\ $$ Commented by sonukgindia last…
Question Number 197110 by cortano12 last updated on 08/Sep/23 Answered by MathematicalUser2357 last updated on 10/Sep/23 $$\mathrm{let}\:{f}\left({x}\right)=\frac{\sqrt[{\mathrm{3}}]{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }−\mathrm{2}\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} +\mathrm{3}}+\sqrt[{\mathrm{3}}]{\mathrm{4}}}{\left({x}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\mathrm{Then}\:\underset{{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}{f}\left({x}\right)=\infty…
Question Number 197111 by cortano12 last updated on 08/Sep/23 $$\:\:\:\:\:\:\cancel{ } \\ $$ Answered by Frix last updated on 08/Sep/23 $$\int\frac{{dx}}{\:\sqrt{\mathrm{cos}^{\mathrm{3}} \:{x}\:\mathrm{sin}^{\mathrm{5}} \:{x}}}\:\overset{{t}=\mathrm{tan}\:{x}} {=} \\…
Question Number 197132 by Erico last updated on 08/Sep/23 $$\underset{\:\mathrm{0}} {\int}^{\:+\infty} \left(\frac{\mathrm{ln}\left(\mathrm{t}+\sqrt{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }\right)}{\mathrm{t}}\right)^{\mathrm{2}} =\frac{\pi^{\mathrm{2}} }{\mathrm{2}} \\ $$ Commented by mnjuly1970 last updated on 09/Sep/23 $$\:\:\:\:{ti}\:{tok}\:{agha}\:{sardool}\:..…